This invention relates generally to projecting images, and more particularly to projecting images onto curved surfaces.
Projector systems have been used to render large images onto display surfaces. With multiple projectors, it is possible to generate even larger seamless displays. Such systems are particularly useful for constructing immersive visualization environments capable of presenting high-resolution images for entertainment, education, training, and scientific simulation. Known multi-projector technologies include Cruz-Neira et al., xe2x80x9cSurround-screen Projection-based Virtual Reality: The Design and Implementation of the CAVE,xe2x80x9d SIGGRAPH 93 Conference Proceedings, Vol. 27, pp. 135-142, 1993, Staadt et al., xe2x80x9cThe blue-c: Integrating real humans into a networked immersive environment,xe2x80x9d ACM Collaborative Virtual Environments, 2000.
A number of techniques are known for generating seamless images on planar surfaces using electro-optical techniques to determine registration and blending parameters, see Li et al., xe2x80x9cOptical Blending for Multi-Projector Display Wall System,xe2x80x9d Proceedings of the 12th Lasers and Electro-Optics Society, 1999, or using a camera in a loop, Surati, xe2x80x9cScalable Self-Calibrating Display Technology for Seamless Large-Scale Displays,xe2x80x9d Ph.D. Thesis, Massachusetts Institute of Technology, 1999, Chen et al., xe2x80x9cAutomatic Alignment of High-Resolution Multi-Projector Displays Using An Un-Calibrated Camera,xe2x80x9d IEEE Visualization, 2000, and Yang et al, xe2x80x9cPixelFlex: A Reconfigurable Multi-Projector Display System,xe2x80x9d IEEE Visualization, 2001, Brown et al., xe2x80x9cA Practical and Flexible Large Format Display system,xe2x80x9d Tenth Pacific Conference on Computer Graphics and Applications, pp. 178-183, 2002, Humphreys et al., xe2x80x9cA Distributed Graphics System for Large Tiled Displays,xe2x80x9d IEEE Visualization, 1999, and Humphreys et al., xe2x80x9cWireGL: A Scalable Graphics System for Clusters,xe2x80x9d Proceedings of SIGGRAPH, 2001.
When multiple projectors are used, an accurate estimation of the geometric relationship between overlapping images is key for achieving a seamless display. The geometric relationship influences the rendering process and soft edge blending. Camera-based methods, which exploit a homography expressed by a 3 by 3 matrix, admit casually installed projectors while eliminating cumbersome manual alignment.
The relationship for surfaces that adhere to quadric equations can be defined using a quadric image transfer function, see Shashua et al., xe2x80x9cThe quadric reference surface: Theory and applications,xe2x80x9d Tech. Rep. AIM-1448, 1994.
Multi-projector alignment for curved surfaces can be aided by projecting a xe2x80x98navigatorxe2x80x99 pattern and then manually adjusting the position of the projectors. For a large scale display, such as used at the Hayden Planetarium in New York, it takes technicians several hours each day to align seven overlapping projectors.
One problem is that when 3D images are displayed on a curved screen, the images are perspectively correct from only a single point in space. This 3D location is known as the virtual viewpoint or xe2x80x98sweet-spotxe2x80x99. As the viewer moves away from the sweet-spot, the images appear distorted. For very large display screens and many view points, it is difficult to eliminate this distortion. However, in real-world applications, viewers would like to be at the exact same place where the projectors ideally need to be located. In addition, placing projectors at the sweet-spot means using a very wide-field of view projectors, which are expensive and tend to have excessive radial or xe2x80x98fish-eyexe2x80x99 distortion.
In another method, a non-parametric process places a camera at the sweet-spot. The camera acquires an image of a structured light pattern projected by the projector. Then, in a trial-and-error approach, samples are taken, to build an inverse warping function between a camera input image and a projected output image by means of interpolation. Then, the function is applied, and resampled until warping function correctly displays the output image, see Jarvis, xe2x80x9cReal Time 60 Hz Distortion Correction on a Silicon Graphics IG,xe2x80x9d Real Time Graphics 5, pp. 6-7, February 1997, and Raskar et al., xe2x80x9cSeamless Projection Overlaps Using Image Warping and Intensity Blending,xe2x80x9d Fourth International Conference on Virtual Systems and Multimedia, 1998.
It is desired to provide a parametric method for aligning multiple projectors that extends the homography-based approach for planar surfaces to quadric surfaces.
In computer vision, some work has been done on using quadric formulations for image transfer functions, see Shashua et al., above, and Cross et al., xe2x80x9cQuadric Surface Reconstruction from Dual-Space Geometry,xe2x80x9d Proceedings of 6th International Conference on Computer Vision, pp. 25-31, 1998. However, the linear methods intended for cameras, as described below, produce large errors when used with projectors, instead of cameras.
In multi-projector systems, several techniques are known for aligning images seamlessly on flat surfaces using planar homography relationships. However, there has been little work on techniques for parameterized warping and automatic registration of images displayed on higher order surfaces.
This is a serious omission because quadric surfaces do appear in many shapes and forms in projector-based displays. Large format flight simulators have traditionally been cylindrical or dome shaped, see Scott et al., xe2x80x9cReport of the IPS Technical Committee: Full-Dome Video Systems,xe2x80x9d The Planetarian, Vol. 28, p. 25-33, 1999, planetariums and OnmiMax theaters use hemispherical screens, Albin, xe2x80x9cPlanetarium special effects: A classification of projection apparatus,xe2x80x9d The Planetarian, Vol. 23, pp. 12-14, 1994, and many virtual reality systems use a cylindrical shaped screen.
Therefore, it is desired to provide calibration methods, quadric transfer functions, and parametric intensity blending for images projected onto a curved display surface.
Curved display screens are increasingly being used for high-resolution immersive visualization environments. The invention provides a method and system for displaying seamless images on quadric surfaces, such as spherical or cylindrical surfaces, using a single or multiple overlapping projectors. A new quadric image transfer function is defined to achieve sub-pixel registration while interactively displaying two or three-dimensional images.